If two shafts are neither parallel nor perpendicular, but include a small angle in the plane that is defined by the axis of rotation, then two possible gearing solutions are known to accomplish a motion transmission.
One possible solution is called Beveloids. Beveloids are manufactured like cylindrical gears using, for example, a hobbing process for soft manufacturing and a threaded wheel grinding for hard finishing. Shaft angles between 0° and about 15° can be realized according to the Beveloid method which results, depending on the ratio, in gear pitch angles between 0° and about 7.5°, or in case of the combination of one conical gear with one conventional cylindrical gear, the maximal required pitch angle might be as high as about 15°.
The second possibility is the application of angular spiral bevel gears. The ratio in most real applications is close to miter which results in pitch angles between 0° and about 7.5°.
The described angular spiral bevel gearsets are used primarily in automotive transfer cases to transmit rotation and torque from the output shaft of a transmission to the front axle of an all wheel driven vehicle.
The mechanical function of both, tapered cylindrical gears (Beveloids) or angular spiral bevel gears is to provide an angle between the shafts in the plane that their two axes define. In most cases concerning all wheel drive vehicles, this will still require two constant velocity joints or two universal joints (one on each end of the drive shaft) in order to connect the output shaft of the gear box with the input shaft of the front axle which commonly have different vertical locations.
In order to connect two points in space, like in case of a propeller shaft between the output of a transfer case and a front axle input, it is necessary to provide one angle and a linear offset or two angles in perpendicular planes. Hypoid bevel gears represent such a general valid solution of input/output shaft orientation in three dimensional space. However, the features of hypoid gears known to date do not cover the case of low shaft angle and high offset. The different hypoid theories applied at present do not allow for the design of low shaft angle bevel gears with any offset. The hypoid theory is based on a flat or conical generating gear as the basis for basic setting and tool parameter calculation. Shaft angles close to and including 90° combined with ratios of 2.5 and higher lead to gear pitch cone angles of about 68° and higher and pinion pitch cone angle of about 22° and lower. This leads to a typical ring gear whose cone is close to a plane, with a tangent plane to the pitch cone which is close enough to the pitch cone in the neighborhood of the contacting line. Such an arrangement allows for the application of certain amounts of hypoid offset, derived in the pitch cone tangent plane according to the traditional hypoid theory.
However, traditional theory fails in cases of high hypoid offsets (close or equal to half the ring gear diameter). The traditional hypoid theory also fails in cases of low ratio (close to 1.0). In cases of high offset, worm gear drives can be used to realize a 90° shaft angle and an offset of half the gear diameter plus half the worm diameter (like center distance in cylindrical gearing). In case of low ratios, crossed helical gears can be used to achieve any desired shaft angle combined with an offset equal the center distance of those crossed helical gears.
The freedom of any small shaft angle (e.g. greater than 0° to 30°) combined with any offset from zero to the sum of half the mean pitch diameters of the two members will be possible with the teachings of the inventive method.